How to Measure the Cosmic Curvature

Abstract

The conventional method to determine the cosmic curvature is to measure the total mass density $Ω_{\rm tot}$. Unfortunately the observational $Ω_{\rm tot}$ is closely near the critical value 1. The computation of this paper shows that $Ω_{\rm tot}\approx 1$ is an inevitable result for the young universe independent of the spatial topology. So the mass density is not a good criterion to determine the cosmic curvature. In this paper, we derive a new criterion based on the galactic distribution with respect to redshift $z$, which only depends on the cosmological principle and geometry. The different type of spatial topology will give different results, then the case can be definitely determined.